We derive fast algorithms for doing signal reconstruction without phase. This type of problem is important in signal processing, especially speech recognition technology, and has relevance for state tomography in quantum theory. We show that a generic frame gives reconstruction from the absolute value of the frame coefficients in polynomial time. An improved efficiency of reconstruction is obtained with a family of sparse frames or frames associated with complex projective 2-designs.

Date Published: 20 September 2007
PDF: 9 pages
Proc. SPIE 6701, Wavelets XII, 67011L (20 September 2007); doi: 10.1117/12.731117

Published in SPIE Proceedings Vol. 6701:
Wavelets XII
Dimitri Van De Ville; Vivek K. Goyal; Manos Papadakis, Editor(s)